Pseudomonomials and ideals generated by pseudomonomials (pseudomonomial ideals) are a central object of study in the theory of neural rings and neural codes. In the setting of a polynomial ring, we define the polarization operation ρ sending pseudomonomials to squarefree monomials and a further polarization operation P sending pseudomonomial ideals to squarefree monomial ideals. We show for a p...

We investigate the rational powers of ideals. find that in case monomial ideals, canonical indexing leads to a characterization yielding symbolic squarefree ideals are indeed themselves. Using connection with techniques, we use splittings show convergence depths and normalized Castelnuovo–Mumford regularities. Stanley for powers, as consequence this, before-now unknown integral closure powers. ...